🧬 biology

Learning Canonical Representations for Unified 3D Molecular Modeling

The paper introduces TheMol, a 3D molecular representation framework that learns a canonical frame to decouple global pose from representation learning, enabling a single unified model to effectively handle diverse tasks like property prediction, coordinate generation, and structure-based optimization while improving rotational stability and latent-space structure.

Original authors: Sanghyun Park, Seungyeon Choi, Hwanhee Kim, yoonju kim, seungyong lee, inpyo hong

Published 2026-07-22

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CC BY 4.0

Original authors: Sanghyun Park, Seungyeon Choi, Hwanhee Kim, yoonju kim, seungyong lee, inpyo hong

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are trying to teach a robot how to understand the shape of a molecule, like a tiny, complex Lego structure. In the world of drug discovery, scientists need these robots to do three very different jobs: guess how strong a molecule is (like predicting its weight), build a brand new molecule from scratch, and tweak an existing one to fit perfectly into a biological lock. The tricky part is that molecules can spin and rotate in space just like a spinning top. If you hand the robot a molecule facing left, then the same molecule facing right, it needs to know they are the same object, not two different ones.

For a long time, scientists have tried to solve this "spinning problem" in three main ways. Some robots ignore the direction entirely, treating the molecule like a cloud of points (great for guessing weight, bad for building). Others try to memorize every possible angle the molecule could spin to (great for building, but the robot gets confused when trying to optimize). A third group just shows the robot the molecule in random spins over and over, hoping it learns to ignore the direction by sheer repetition (simple, but the robot might still get tripped up by a new angle). The big question is: Can we build one single, super-smart robot brain that handles all three jobs without getting confused by the spinning?

This is exactly what the researchers at Yonsei University tackled in their new paper introducing a system called THEMOL. Think of THEMOL as a clever new trick for teaching the robot. Instead of forcing the robot to memorize every spin or ignore the direction completely, THEMOL teaches the molecule to "stand up straight" before the robot even looks at it.

Here is how it works: Imagine you have a wobbly, spinning toy. Before you try to describe it or build a copy, you gently grab it and place it on a table in a specific, standard pose—let's say, with its "head" pointing north and its "feet" pointing south. THEMOL does this digitally. It learns a special rule to rotate any molecule into this perfect, "canonical" (standard) pose instantly. Once the molecule is standing in this standard pose, the robot's brain (which is actually quite simple and doesn't need to worry about spinning anymore) can easily learn the molecule's true shape and chemical secrets.

The paper suggests that this approach is a game-changer because it separates the "spinning" problem from the "learning" problem. By cleaning up the orientation first, the system creates a single, shared memory space where molecules are organized by their chemistry, not by which way they were facing when they arrived.

The researchers tested this idea and found some exciting results. They showed that THEMOL can predict chemical properties just as well as the best existing models, but it also does a much better job at generating new 3D structures that look physically real. Perhaps most importantly, when they tried to "optimize" molecules (tweaking them to work better), THEMOL didn't waste time spinning the molecules around in circles; it focused purely on changing the chemistry. In their tests, THEMOL achieved top scores on 6 out of 9 standard chemical prediction datasets and generated molecules with 99.9% validity, meaning almost every molecule it built was chemically possible.

The authors suggest that this method offers a more stable and efficient way to handle 3D molecules. While they admit that for extremely symmetrical or floppy molecules, finding the perfect "standard pose" can still be a little tricky, the results indicate that teaching a model to align molecules first creates a much stronger foundation for future drug discovery tools. It's like realizing that to build a perfect house, you don't need to memorize every possible angle the blueprint could be held at; you just need to lay the blueprint flat on the table first.

Technical Summary: Learning Canonical Representations for Unified 3D Molecular Modeling

Problem Statement

Three-dimensional molecular foundation models are increasingly expected to support a diverse range of tasks, including scalar property prediction, coordinate generation, and structure-based optimization. However, these tasks impose conflicting geometric-symmetry requirements on the learned representations:

Scalar prediction typically benefits from invariant representations that discard global pose.
Coordinate generation and force prediction require equivariant representations that preserve transformation structures.
Rotation-augmented non-equivariant models attempt to learn robustness statistically but often fail to guarantee single-view stability or require expensive multi-view inference.

Existing approaches typically choose one strategy, which creates specific trade-offs when a single pretrained latent space is reused across heterogeneous tasks. Invariant models discard chirality-sensitive signals and require complex lifting mechanisms for coordinate reconstruction. Equivariant models entangle global orientation with chemical variation, complicating latent-space generation and optimization by mixing gauge changes with meaningful structural changes. Rotation-augmented models lack guaranteed stability across all orientations. Furthermore, evaluating representation quality solely through downstream benchmark scores is insufficient, as it can be confounded by task-specific heads and fine-tuning protocols.

Methodology: THEMOL

The authors introduce THEMOL, a framework that separates global pose handling from representation learning through learned canonicalization.

Core Architecture

Canonical Frame Learning: Before encoding, THEMOL maps rotated copies of a molecule to a shared canonical pose. This is achieved by learning a rotation selector $\hat{R}_\theta(x, h) \in SO(3)$ $\hat{R}_{θ} (x, h) \in S O (3)$ that aligns the centered coordinates $x_c$ $x_{c}$ to a consistent frame.
- The canonicalized coordinates are defined as $A_\theta(x, h) = x_c \hat{R}_\theta(x, h)^\top$ .
- The system enforces gauge consistency: $A_\theta(xR^\top, h) = A_\theta(x, h)$ , ensuring that global rotations are removed before the backbone processes the input.
Non-Equivariant Backbone: A standard non-equivariant transformer autoencoder operates on these canonicalized coordinates. Because the input is already aligned, the backbone does not need to learn equivariance or invariance explicitly; it simply learns the distribution of molecular structures in a consistent coordinate system.
Unified Output Handling:
- Invariant Outputs: Scalar predictions are read directly from the canonical latent space.
- Equivariant Outputs: Coordinate-level predictions are generated in the canonical frame and then "lifted" back to the original coordinate system using the selected rotation $\hat{R}_\theta$ .

Evaluation Strategy

Beyond standard downstream benchmarks, the authors propose a suite of intrinsic representation diagnostics to evaluate the frozen latent space directly:

Molecular Identity Preservation: Measured by AUC.
Chemical Semantic Coherence: Assessing if similar molecules cluster correctly.
Effective Dimension: Evaluating the utilization of the latent space.
Hubness and Uniformity: Measuring the geometric structure of the embedding space.
Pretrain-Finetune Alignment: Comparing principal subspaces to ensure downstream adaptation follows pretraining variation directions.
Task-Readiness Diagnostics: Including rotation sensitivity, latent-distance hierarchy (distinguishing rotation from conformational changes), decodability under perturbation, and optimization efficiency (measuring "gauge waste").

Key Results

1. Representation Quality and Stability

Rotational Stability: THEMOL collapses randomly rotated copies of a molecule into a compact embedding cluster, significantly outperforming rotation-augmented baselines (Repr.C) which show dispersed embeddings.
Latent Organization: The latent space exhibits a clear hierarchy where rotations induce the smallest displacement, followed by conformational changes, matched-molecular-pair (MMP) changes, and scaffold differences. This indicates that canonicalization successfully separates nuisance pose variation from chemically meaningful structural variation.
Decodability & Optimization: THEMOL maintains higher validity (PB-Valid) under latent perturbations and interpolation compared to equivariant or augmentation-based models. In optimization tasks, it demonstrates lower "gauge waste" (displacement along rotation-induced directions) and higher search efficiency.

2. Downstream Performance

THEMOL was evaluated on three distinct task families using a single pretrained latent space:

Scalar Property Prediction: On MoleculeNet (9 datasets), THEMOL achieved the highest mean ROC-AUC (81.65), ranking first on six datasets. On the TDC ADMET benchmark (22 tasks), it achieved a mean rank of 3.4, outperforming the TDC leaderboard SOTA and MiniMol on 15 tasks.
3D Molecule Generation: On GEOM-DRUG, THEMOL achieved 86.8% atom stability and 99.9% validity under the v1 protocol. Under stricter v2 metrics, it achieved the highest PB-Valid (93.7%) and lowest median relaxation displacement ( $\Delta R_{relax}$ ), indicating physically realistic geometries.
Structure-Based Optimization: On CrossDocked2020, THEMOL achieved the strongest predicted binding affinity (best average SMINA and Vina Dock scores) while maintaining the highest molecular diversity and competitive synthetic accessibility (SA).

Significance and Claims

The paper claims that the primary advantage of THEMOL is not isolated task-specific superiority, but the cross-task stability of a single canonical latent space. By treating global pose as an interface variable rather than a burden carried throughout the representation, THEMOL enables a non-equivariant backbone to be reused effectively for:

Invariant tasks (scalar prediction) without losing coordinate-level information.
Equivariant tasks (generation/optimization) without entangling orientation with chemical variation.

The authors argue that this design resolves the symmetry-induced trade-offs inherent in invariant, equivariant, and augmentation-based approaches. They emphasize that reusable 3D molecular representations must be evaluated not just by downstream scores, but by their intrinsic geometric stability, chemical organization, and ability to support modeling operations like interpolation and property-guided search. THEMOL demonstrates that explicitly separating global pose from molecular variation provides a principled route to foundation models that can be deployed across tasks with differing geometric requirements.

Limitations

The authors acknowledge that learned canonical frames may be ambiguous for highly symmetric, near-degenerate, or highly flexible molecules. The current study focuses on small-molecule modeling; extending this to peptides, proteins, and protein-ligand complexes would require handling larger conformational variability and multiple interacting coordinate frames. Additionally, structure-based optimization was evaluated using docking-based proxies rather than experimental binding affinity.